An inverse analysis of warpage for trilayer thin-plate under thermal cycles

Thermal–mechanical behavior of a trilayer plate with micro-scale layer thicknesses is investigated using the hybrid experimental analytical inverse method (HEAIM). This study adopts and modifies an existing analytical solution by Suhir to evaluate the warpage of trilayer structures consisting of a mid-layer comparable in thickness and mechanical properties to other layers under thermal cycles. A phase-shifted shadow moiré is employed to obtain accurate measurements of the plate thermal warpage during a thermal cycle. The measurements are then inversely analyzed following a numerical approach that finally determines those uncertain material parameters of the thermal and mechanical properties for the layered plates. If all the material parameters are known, the behavior of the trilayer structure can be further evaluated analytically with enhanced certainty. HEAIM was employed to characterize and evaluate the thermal and constitutive behavior of substrate trilayer structure and its constituent materials under a thermal cycle. The proposed method can provide pertinent guidance to the modeling and design of complex trilayer structures.